Parallel Resistor Calculator

This parallel resistor calculator is a tool for determining the equivalent resistance of a circuit with up to ten resistors in parallel. On the other hand, you can also check out our series resistor calculator if you want to learn about resistors in series.

Prefer watching over reading? Learn all you need in 90 seconds with this video we made for you:

A parallel circuit is characterized by a common potential difference (voltage) across the ends of all resistors. The equivalent resistance for this kind of circuit is calculated according to the following formula:

Where:

• $R$ – Equivalent parallel resistance; and
• $R_1$, $R_2$, ..., $R_n$ – Resistances of individual resistors numbered $1$, $2$, to $n$.

The units of all values are Ohms (symbol: $\small \Omega$). 1 Ohm is defined as electrical resistance between two points that, when applied with a potential difference of 1 volt, produces a current of 1 ampere. Hence, $\small 1\ \Omega = 1\ \text{V} / 1\ \text{A}$ or, in SI base units, $\small \Omega = \text{kg} \cdot \text{m}^2/(\text{s}^3 \cdot \text{A}^2)$.

The formula for resistors in parallel is similar to the formula for inductors in parallel.

The parallel resistor calculator has two different modes. The first mode allows you to calculate the total resistance equivalent to a group of individual resistors in parallel. In contrast, the second mode allows you to set the desired total resistance of the bunch and calculate the one missing resistor value, given the rest.

To keep it simple, we only show you a few rows to input numbers, but new fields will magically appear as you need them. You can input up to 10 resistors in total.

Let's look at an example for the second, slightly more complicated, mode:

1. Select Calculate missing resistor under Mode.
2. Now input the total resistance you want your circuit/collection of resistors to have.
3. Start by introducing the values of the resistors you already know (new fields will appear as needed).
4. The calculator automatically gives you the required missing resistor after each input.

Knowing how the parallel resistors arrangement work makes it possible to apply the current divider rule in the circuit.

The principle is the same as when determining capacitance in series or induction in parallel – you can use it for these calculations too. Just remember that the units are not the same!

If you would like to find out the value of power dissipated in the resistor, try the Ohm's law calculator or resistor wattage calculator.

To calculate the equivalent resistance of two resistors in parallel:

1. Take their reciprocal values.

2. Add these two values together.

3. Take the reciprocal again.

For example, if one resistor is 2 Ω and the other is 4 Ω, then the calculation to find the equivalent resistance is:

1 / (¹/₂ + ¹/₄) = 1 / (³/₄) = ⁴/₃ = 1.33 Ω.

Yes, the voltage across all the components is the same in a parallel circuit, while the current is divided among all of them.

This phenomenon happens because the current has many more paths that it could take. Imagine a shop opens up several new check-out tills. The overall resistance to people going through the check-out will decrease as the workload is shared in parallel.

Rearrange the parallel resistor formula 1/R = 1/R₁ + 1/R₂ + … + 1/R_n in terms of R_n, given that you know the desired overall resistance. That gives you R_n = (1/R - 1/R₁ + 1/R₂ + …)^-1

For example, if you have R₁ = 4 Ω, R₂ = 2 Ω and want R = 1 Ω, then R₃ = 1 / (1 - ¹/₄ - ¹/₂) = 4 Ω.